Explain the concept of options Greeks and their application in managing risk and understanding the sensitivity of options prices to various market factors.

Options Greeks are a set of five key metrics that measure the sensitivity of an option's price to different market factors. These factors include the underlying asset's price, time until expiration, volatility, and interest rates. Understanding and using these Greeks allows options traders to better manage risk and make informed trading decisions. 1. Delta: This Greek measures the change in the option's price for every $1 change in the underlying asset's price. A delta of 0.5 means the option price will increase by $0.50 for every $1 increase in the underlying asset's price. Delta is always between 0 and 1 for call options and between -1 and 0 for put options. For example, a call option with a delta of 0.7 will track 70% of the underlying asset's price movements, while a put option with a delta of -0.3 will move 30% in the opposite direction of the underlying asset's price. 2. Gamma: This Greek measures the rate of change of the option's delta. It tells you how much the delta will change for every $1 change in the underlying asset's price. A higher gamma means the delta is more sensitive to changes in the underlying asset's price. This is particularly important for options that are at or near the money, as their delta can change rapidly. For example, a ....